Parameterized complexity of the list coloring reconfiguration problem with graph parameters

Tatsuhiko Hatanaka, Takehiro Ito, Xiao Zhou

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Let G be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of k colors. For two given list colorings of G, we study the problem of transforming one into the other by changing only one vertex color assignment at a time, while at all times maintaining a list coloring. This problem is known to be PSPACE-complete even for bounded bandwidth graphs and a fixed constant k. In this paper, we study the fixed-parameter tractability of the problem when parameterized by several graph parameters. We first give a fixed-parameter algorithm for the problem when parameterized by k and the modular-width of an input graph. We next give a fixed-parameter algorithm for the shortest variant which computes the length of a shortest transformation when parameterized by k and the size of a minimum vertex cover of an input graph. As corollaries of these two results, we show that the problem for cographs and the shortest variant for split graphs are fixed-parameter tractable even when only k is taken as a parameter. On the other hand, we prove that the problem is W[1]-hard when parameterized only by the size of a minimum vertex cover of an input graph.

Original languageEnglish
Pages (from-to)65-79
Number of pages15
JournalTheoretical Computer Science
Volume739
DOIs
Publication statusPublished - 2018 Aug 29

Keywords

  • Combinatorial reconfiguration
  • Fixed-parameter algorithm
  • Graph algorithm
  • List coloring
  • W[1]-hardness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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